Auctions with endogenous participation

We study endogenous-participation auctions where bidders only know the number of potential participants. After seeing their values for the object, potential participants decide whether or not to enter the auction. They may not want to enter the auction since they have to pay participation costs. We characterize equilibrium bidding strategies and entry decisions for both first- and second-price sealed-bid auctions when participation is endogenous. We show that there is a pure strategy entry equilibrium where only bidders with values greater than a certain cut-off point actually bid. In this context, both types of auctions generate the same expected revenue. We also show that, contrary to the predictions of the fixed number of bidders literature, the seller's expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts with results from the existing literature on auctions with entry. As in the fixed-n literature, we show that first-price auctions generate more expected revenue than second-price auctions when buyers are risk-averse. Finally, we characterize the optimal auction – the auction that maximizes the seller's expected revenue – by using a direct revelation mechanism. The optimal auction involves a reserve price larger than the optimal reserve price in the fixed-n literature. The winner's payment is the second highest bid less the participation cost and losers receive a subsidy equal to the participation cost. Received: 17 August 1998 / 21 September 1999     

Auctions with asymmetric common-values: The first-price format

We study the performance of the first-price format in auctions with asymmetric common-values. We show that, contrary to the result for second-price auctions, a small advantage for one player translates only to small changes in bidders’ strategies, and the equilibrium remains close to the first-price equilibrium of the original game. We characterize the equilibrium bidding strategies and their behavior as the degree of asymmetry increases. Finally, we compare the revenues at the optimal auction, the first-price auction and the second-price auction.     

Optimal auctions and information disclosure

We characterise properties of optimal auctions if the seller may disclose information about the quality of the object for sale. We show that the seller maximizes his expected revenue by revelation of all information to all bidders and implementing a second price auction with appropriate reservation price.     

Wars of attrition and all-pay auctions with stochastic competition

We extend the war of attrition and all-pay auction analysis of Krishna and Morgan (1997) to a stochastic competition setting. We determine the existence of equilibrium bidding strategies and discuss the potential shape of these strategies. Results for the war of attrition contrast with the characterization of the bidding equilibrium strategies in the first-price all-pay auction as well as the winner-pay auctions. Furthermore we investigate the expected revenue comparisons among the war of attrition, the all-pay auction and the winner-pay auctions and discuss the linkage principle as well. Our findings are applicable to future works on contests and charity auctions.     

Anticipation of Auction Fever: Entry Decision,Reserve Price and the Choice of Auction Design

This paper analyzes the entry decision of rational bidders who expect to experience auction fever in English auctions. It shows that nonparticipation decision reduces seller's expected profit and this effect may outweigh the positive effect of the auction fever. We analyze the choice between English and second‐price sealed‐bid auctions and the optimal reserve price in English auctions. We show that it might be optimal for the seller to set a reserve price below her own valuation of the object. Finally, we show that the order in which bidders place their bids matters and the first bidder always has an advantage. Copyright © 2011 John Wiley & Sons, Ltd.     

Common value auctions with independent types

In this paper I consider a common value model, with independent types, where the ex-post value of the good is influenced by the bidders' information at the auction stage. The seller cannot fully extract the surplus. In a symmetric model the optimal mechanism can be implemented through first price, second price, or English auctions; but not through a Dutch auction. Other properties of the optimal auctions are that the seller's reservation price is endogenous, and that in sealed bid auctions the price may exceed the value of the object (winner's curse).     

Auctions with resale and bargaining power

We show that when the weak bidder’s bargaining power in the resale market is weakened, the auctioneer’s revenue from the first-price auction with resale is lower. Using the idea of Coase Theorem, we show that when the resale market is a sequential bargaining model with no commitment, the auctioneer’s revenue is substantially reduced, and the ranking is the opposite of Hafalir and Krishna (2009). We establish a version of the Coase Theorem in the context of the auctions with resale. When Coase Theorem holds, we show that the revenue of the auction with resale is lower than the revenue of the same auction without resale. We also provide the existence and uniqueness of equilibrium for our model of auctions with resale.     

Corners in Auctions

Different pricing rules in multiunit auctions provide different incentives for a bidder to corner the auction and thus require different levels of effort from the seller to deter cornering. We consider three different types of auctions: the pay-your-bid or "discriminatory" auction commonly used by the US Treasury, the lowest-winning-bid uniform-price auction used in the current Treasury experiment, and the highest-losing-bid uniform-price auction considered by Vickrey almost four decades ago. We show that the pay-your-bid auction provides the greatest incentive to corner the market, that the experimental Treasury auction provides less incentive, and that the highest-losing-bid uniform-price auction provides the least. Arguably, the less the incentive to corner the market, the easier it will be for sellers to deter cornering, and the greater their expected revenue (net of the cost to deter cornering) will be in otherwise expected-revenue-equivalent auctions.     

He who must not be named

Landsberger et al. have studied a sealed bid first price auction with two players in which the ranking of the valuations is known. They argue that such a situation can arise in a sequential auction where only the name of the winner is revealed. In this paper we consider sequential auctions where two identical goods are sold sequentially to N players who are interested in both objects. In sealed bid auctions, no information is a priori revealed by the mechanism, but the seller can in principle reveal whatever he wants. We restrict our attention to the case where only the name of the winner is revealed to be in the context of Landsberger et al. for the second auction. The aim of the paper is to compare such a sequential auction with a simultaneous auction where both goods are sold as a bundle or equivalently with a sequential auction where no information is revealed. We first show that there exists an equilibrium of the sequential game in pure and monotone strategies. Then, the comparison of the seller's expected revenue in the two cases allows us to conclude that contrary to Landsberger et al.'s predictions, the seller can not use the information to increase his revenue. This result is obtained using simulations for a large class of distribution functions. The seller must not reveal the name of the winner between the two auctions and instead sell both goods using a simultaneous auction.Received: 31 July 2001, Accepted: 5 February 2003, JEL Classification: B44I wish to thank Laurent Linnemer, Thomas Ricke, Michael Visser and Shmuel Zamir for helpful comments and suggestions. I am very grateful to the referees and the associated editors in charge of my paper.     

Calibration of a model of declining prices in cattle auctions

Using data from dairy cattle auctions plus independent appraisals of the cattle sold, this paper is able to verify the existence of the “declining price anomaly”: prices decline over the course of the auction, with the main decline occurring towards the end of the day. We show that the data are consistent with a simple model of sequential auctions of goods with independent values, and examine distributions which replicate the important features of the data. The crucial feature driving the price declines in the model is a limited capacity for purchases by the participants in the auction, which in turn decreases competition for the final units in the auction.     

Optimal fees in internet auctions

An auction house runs a second-price auction with a possibility of resale through re-auctions. It collects listing and closing fees from the seller. We find the fees which maximize the revenue of the auction house. In particular, we show that the optimal listing fee is zero. Our findings are consistent with the policies of eBay, Amazon, Yahoo, and other Internet auctions.      

AUCTIONS: AN INTRODUCTION

Abstract. This is a detailed introduction to auction theory. It begins with a simple analysis of standard auctions and then uses a strikingly simple general solution of symmetric private values auctions to prove the payoff equivalence of many auction rules. The basic framework is then modified to admit risk aversion, multi-unit and repeated auctions as well as collusion. Then follows an introduction to optimal auctions, with and without stochastic entry, and to common value auctions and the winner's curse problem. The survey closes with a sample of applications, from the regulation of natural monopolies to price competition in oligopoly and the government securities market.     

Learning through Simultaneous Play: Evidence from Penny Auctions

This paper contributes to the emerging empirical literature on penny auctions, a particular type of all‐pay auctions. We focus on the potential learning effects that bidders may experience over time but also (and particularly) across auctions as a result of their auction participation. Using detailed bid‐level information, we find that, similarly to earlier literature, bidders suffer from a sunk cost fallacy, whereby their probability of dropping out of an auction is decreasing in the number of bids they have already placed in that auction. Although we do find that learning through repeated participation alleviates the sunk cost fallacy, participation in simultaneous penny auctions emerges as a much more effective learning mechanism, ultimately contributing toward bidders earning higher individual surpluses.     

Econometric models of asymmetric ascending auctions

We develop econometric models of ascending (English) auctions which allow for both bidder asymmetries as well as common and/or private value components in bidders’ underlying valuations. We show that the equilibrium inverse bid functions in each round of the auction are implicitly defined (pointwise) by a system of nonlinear equations, so that conditions for the existence and uniqueness of an increasing-strategy equilibrium are essentially identical to those which ensure a unique and increasing solution to the system of equations. We exploit the computational tractability of this characterization in order to develop an econometric model, thus extending the literature on structural estimation of auction models. Finally, an empirical example illustrates how equilibrium learning affects bidding during the course of the auction.     

在线拍卖中的代理研究综述

在线拍卖站点的不断增加给在线竞买人提出了具大的挑战,竞买人需要从大量的拍卖站点中选择一个恰当的拍卖站点,以保证在满足他们偏好的前提下得到他们希望的物品。不同的拍卖站点采用的拍卖方式和竞价策略是不同的,因此,不同的拍卖站点其竞价代理的设计策略也不同。本文主要对目前在线拍卖代理研究进行综述。     

Revenue comparison of discrete private-value auctions via weak dominance

We employ weak dominance to analyze both first-price and second-price auctions under the discrete private-value setting. We provide a condition under which the expected revenue from second-price auction is higher than that of first-price auction. We also provide implications for large auctions, including the “virtual” revenue equivalence.     

The Buyer's Option in Multi-Unit Ascending Auctions: The Case of Wine Auctions at Drouot

This paper studies multi-unit ascending (English) auctions with a buyer's option. The buyer's option gives the winner of an auction the right to purchase any number of units at the winning price. We develop a theoretical model and derive the optimal strategies for the bidders. The model predicts various behavioral implications (e.g., the winner never exercises the option, the price declines…) that are tested using a unique data set on wine auctions held at the Paris-based auction house Drouot. We also analyze why the buyer's option is used. Estimating the model in a structural econometric way, and using counterfactual comparisons, we find that the buyer's option does not affect the seller's revenue (relative to a system where the units are auctioned sequentially without the option). Drouot, however, saves a lot of time with the option and this effect represents a considerable amount of money. The time-saving effect seems thus to be the primary purpose of the buyer's option.     

The impact of reserve prices on the perceived bias of expert appraisals of fine art

We examine whether expert appraisals provided to bidders before major art auctions are unbiased indicators of value. Despite a strong grounding in theory, this aspect of optimal auction design has been frequently challenged in previous empirical research, particularly in the market for fine art. We adopt a valuation benchmark that incorporates sellers' reserve prices as well as high bids, and recognize censoring of works that fail to make reserve. Although the auction houses never divulge reserve prices, we exploit the fact that they can be observed indirectly via their impact on buy‐in rates. Using the set of French Impressionist paintings brought to auction from 1985 to 2001, we estimate the distribution of reserve prices, establish their link to a proper valuation benchmark, and isolate the selection bias due to bought‐in works on the perceived market value of fine art works. After controlling for the impact of reserve prices, and considering all works brought to auction, we find no evidence of bias in the experts' pre‐sale estimates. Copyright © 2010 John Wiley & Sons, Ltd.     

NONPARAMETRIC ESTIMATION OF ENTRY COST IN FIRST‐PRICE PROCUREMENT AUCTIONS

In this paper, I investigate Samuelson's low‐price auction model with entry costs. The model's equilibrium implies that the distribution of bids is truncated at the threshold for participation. I use the model to estimate the cost of participation in Michigan highway procurement auctions. The null hypothesis of zero entry costs is rejected. Using my empirical results, I then construct an estimate of the optimal auction, which employs regular policy tools such as entry fees. Finally, I demonstrate the savings that the Michigan government could have made on payments if optimal auctions had been employed. Copyright © 2012 John Wiley & Sons, Ltd.     

Identification and estimation in sequential,asymmetric, English auctions

Within the independent private-values paradigm, we derive the data-generating process of the winning bid for the last unit sold at multi-unit, sequential, asymmetric, English auctions. When the identity of the winner and the number of units won by each bidder in previous stages of the auction are observed, we demonstrate nonparametric identification and propose a semi-nonparametric estimation strategy based on orthogonal polynomials. We apply our estimator to daily data from fish auctions in Denmark. For single-unit supply, we use our estimates to compare the revenues a seller could expect to earn were a Dutch auction employed instead.